A PERFORMANCE COMPARISON BETWEEN THE CRAY-YMP2 AND THE ORIGIN2000

By: Steven Ramey

In my study, I have compared the performance of the two machines on
identical code that solves the time dependent Laplace equation in the
context of two dimensional heat conduction. The problem consists of a
square piece of insulating material one meter square with boundary
conditions of 400C and 0C on opposite sides. Two separate methods were
compared on the two machines, one being an explicit solution to the
system of linear equations and the other a simple implicit method
known as simultaneous displacements. Both codes employed a 200X200
mesh and used a time step of 5000 seconds.

The Hardware Performance Monitor (hpm) on the Cray uses on-chip
counters to determine performance statistics such as number of
floating point operations, cpu cycles, and MFLOP (Millions of Floating
Point Operations) rate. Using the information from the hpm utility I
was able to estimate the performance on the Origin 2000 by referencing
the system clock to get run times.

The explicit method ran much faster on both machines due to the
fewer number of operations required (~9.4 billion). As a result, the
Cray was able to execute the code in 47.4 seconds running at 200.3
MFLOP/s. The Origin 2000 was able to distribute the job over eight of
its ten processors and thus was able to run the job in just 9.0
seconds. Since the codes were identical, the same number of operations
must have been performed so the Origin 2000 was operating at over 1
GFLOP/s (Billion Floating Point Operations per second).

The simultaneous method required 256 billion operations to complete
the job due to the iterative nature of the method. As a result, the
Cray machine required 1158.2 seconds to complete the job, but was able
to increase its performance to 221.14 MFLOP/s. The new Origin 2000
machine completed the same job in just 207.0 seconds which means that
it was performing floating point operations at a rate of 1.23
GFLOP/s.

A fundamental challenge of any numerical method relates to the
accuracy of the answer, since in the end all numerical methods are an
approximation to the actual solution. Furthermore, different methods
and different machines will end up predicting a different answer based
on machine architecture and compiler implementation. To test the
consistency between the machines, I checked the value of the center
mesh point after the programs finished. The value obtained by the
explicit method varied by 0.00652% between the machines and the value
from the simultaneous method differed by 0.01088%.